Shanahan has been with Washington since 2010, but is under pressure with his team languishing at the bottom of the NFC East, and their playoff hopes in tatters.
However, Hall has said that the Redskins would be making a poor decision if they were to fire their coach of four years.
He told the Washington Post: "I absolutely would endorse these guys and coaches. I think a big part of success is to have some stability. I think anybody who has had success in this league would tell you that.
"I think the biggest ingredient was just getting the right guys and I think we've done that. We've just got to finish out as strong as possible. Then next year I'm definitely looking forward to this team just being a contender for years to come."
Hall left the Redskins at the end of last season but re-signed with the team in the off-season after several conversations with Shanahan and his team.